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Andrews [41]
3 years ago
12

some of the steps in the derivation of the quadratic formula are shown. step 3: –c b^2/4a=a(x^2 b/ax b^2/4a62) step 4a: –c b^2/4

a=a(x b/2a)^2 step 4b: -4ac/4a b2/4a=a(x b/2a)^2 which best explains or justifies step 4b? -factoring a polynomial -multiplication property of equality -converting to a common denominator -addition property of equality
Mathematics
2 answers:
Dmitrij [34]3 years ago
6 0

Answer:  (c) converting to a common denominator.

Step-by-step explanation: Our quadratic equation ax^{2} +bx+c=0,~a\neq 0 can be solved as follows -

ax^{2} +bx+c=0\\\\\Rightarrow x^{2} +\dfrac{b}{a}x+\dfrac{c}{a}=0,~\textup{since}~a\neq 0\\\\\Rightarrow x^{2} +\dfrac{b}{a}x=-\dfrac{c}{a}\\\\\Rightarrow x^{2} +2\times \dfrac{b}{2a}+\dfrac{b^2}{4a^2}=\dfrac{b^2}{4a^2}-\dfrac{c}{a}\\\\\Rightarrow (x+\dfrac{b}{2a})^2=\dfrac{b^2-4ac}{4a^2}\\\\\Rightarrow x+\dfrac{b}{2a}=\dfrac{\pm\sqrt {b^2-4ac}}{2a}\\\\\Rightarrow x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.

So, according to the given information, the step 4b explains the process of conversion of the terms on both sides to make the denominators same.

Thus, the correct option is (c) converting to a common denominator.



wel3 years ago
3 0
-converting to a common denominator

The terms -c of the left side was converted to -4ac/4a to have the same denominator of b^2/4a.
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Step-by-step explanation:

If we look closely at the sequence we can see:

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We can see a pattern. To get next terms, we add 3, to get next to that, we subtract 2. It goes on like this.

Since 4th term to 5th term is "subtracting 2", logically 5th to 6th term (the term we are wanting) should be "add 3". So the term after 8 would be 11

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3 years ago
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